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A problem by ankush tiwari

Level
pending

Two circles of radii 9 and 16 units touch each other externally. Let \(r\) be the radius of a circle which touches these two circles as well as the common tangent to the two circles. The value of \(r\) can be expressed as \(\frac{a}{b}\) where \(a\) and \(b\) are positive coprime integers. Find \(a + b\).